Ciro Santilli @cirosantilli 37

Types:

Linear combination of a Dirichlet boundary condition and Neumann boundary condition at each point of the boundary.

Examples:

Collection of coordinate charts.

The key element in the definition of a manifold.

Some criticisms:

Every Lie algebra corresponds to a single simply connected Lie group.

The Baker-Campbell-Hausdorff formula basically defines how to map an algebra to the group.

Bibliography:

Techniques to get numerical approximations to numeric mathematical problems.

The entire field comes down to estimating the true values with a known error bound, and creating algorithms that make those error bounds asymptotically smaller.

Not the most beautiful field of pure mathematics, but fundamentally useful since we can't solve almost any useful equation without computers!

The solution visualizations can also provide valuable intuition however.

Important numerical analysis problems include solving:

AGI-complete in general? Obviously. But still, a lot can be done. See e.g.: